共查询到20条相似文献,搜索用时 140 毫秒
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考虑一个用周期力驱动的Duffing方程描叙的囚禁离子云系统,研究初始条件对其同宿轨道混沌行为的影响.结果表明,在各参数满足控制条件的情况下,初始条件的不同,将使轨道处于混沌或有序的不同状态. 相似文献
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本文对带强迫振动项的三分子模型,在强迫振动的幅度C=0.05和频率D一些取值下,进行了数值计算。通过数据分析,给出了2n周期分叉序列,并与Feigenbaum常数δ进行了比较。
关键词: 相似文献
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海阔 《原子与分子物理学报》2007,24(1):85-90
射频阱中离子云与检测场的相互作用由周期驱动的Duffing方程描述.本文报道了该方程的一个精确的周期解,它描述了阱参数和外场对离子云周期运动的影响.结果表明,在各参变量满足周期解条件时,离子的运动频率为外场频率的三分之一,运动振幅分别与外场频率、振幅以及阱频正相关,与离子阱的非谐参数反相关. 相似文献
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《物理学报》2017,(6)
根据非线性局部Lyapunov指数方法,分别以常数强迫Lorenz系统和准周期强迫Lorenz系统为例,研究了在外强迫存在的条件下混沌系统可预报性的改变.结果表明:外强迫会影响混沌系统的可预报性,两种不同类型的强迫Lorenz系统的可预报期限都随着外强迫的增强而增加,但是大小相等方向相反的外强迫对系统可预报性的影响不同,其中正值强迫比负值强迫作用下的可预报期限更长,并且这种差异随着强度的增加而增大;不同形式的外强迫对可预报性的影响也不同,常数强迫的影响主要体现在误差增长的线性阶段,准周期强迫的影响除了线性阶段还必须考虑到非线性阶段;当强度相等的常数强迫和准周期强迫驱动Lorenz系统时,常数强迫作用下的系统可预报性更高.本文基于混沌理论模型的研究,对于实际大气的可预报性研究具有一定的启示意义. 相似文献
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建立了一类含Davidenkov滞后环的非线性相对转动动力学方程.分别分析了该非线性相对转动自治方程和微外扰下非自治方程的分岔特性,并采用KBM法求解了滞后环指数n=2时该非线性相对转动方程在周期激励下的解析近似解.通过数值仿真,得到了几种分岔结构及外扰下全局分岔图,同时将数值解与本文KBM法求解结果进行比较,证明本文求解结果有较高的精度,为研究这一类滞后相对转动系统提供了理论参考依据.
关键词:
相对转动
滞后环
分岔
KBM法 相似文献
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《Physics letters. A》1988,130(2):73-80
When the typical pattern size is used as a bifurcation parameter, partial differential equations modeling pattern formation possess a scaling law. We exploit this scaling law in the prediction of the complex bifurcation structure typically observed in such systems. The Kuramoto-Sivashinsky equation with periodic boundary conditions is used as an illustrative example. 相似文献
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We study the behavior of a Frisch-Hasslacher-Pomeau lattice gas automaton under the effect of a spatially periodic forcing. It is shown that the lattice gas dynamics reproduces the steady-state features of the bifurcation pattern predicted by a properly truncated model of the Navier-Stokes equations. In addition, we show that the dynamical evolution of the instabilities driving the bifurcation can be modeled by supplementing the truncated Navier-Stokes equation with a random force chosen on the basis of the automaton noise. 相似文献
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At weak force range the two-well Duffing equation has a closed bifurcation region in theparameter plane, inside which there are many different periodic windows. By means ofone-dimensional and two-dimensional symbolic dynamics, these periodic windows and thedynamical behavior of chaotic attractors are analyzed systematically. 相似文献
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Frequency-sensitive stochastic resonance in periodically forced and globally coupled systems 总被引:1,自引:0,他引:1
J. Xiao G. Hu H. Liu Y. Zhang 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(1):133-138
A model of globally coupled bistable systems consisting of two kinds of sites, subject to periodic driving and spatially uncorrelated
stochastic force, is investigated. The extended system models the competing process of activators and suppressers. Analytical
computations for linear response of the system to the external periodic forcing is carried out. Noise-induced Hopf bifurcation
is revealed, and stochastic resonance, sensitively depending on the frequency of the external forcing, is predicted under
the Hopf bifurcation condition. Numerical simulations agree with the analytical predictions satisfactorily.
Received: 5 September 1997 / Revised: 13 May 1998 /
Accepted: 18 May 1998 相似文献
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Yoshisuke Ueda 《Journal of statistical physics》1979,20(2):181-196
This paper deals with turbulent or chaotic phenomena which occur in the system governed by Duffing's equation, a special type of two-dimensional periodic system. By using analog and digital computers, experiments are carried out with special reference to the change of attractors and of average power spectra of the random processes under the variation of the system parameters. On the basis of the experimental results, an outline of the random process is made clear. The results obtained in this paper will be applied to various physical problems and will also serve as material for the development of a proper mathematics of this phenomenon. 相似文献
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This paper presents detailed numerical results of the competitive diffusion Lotka-Volterra equation (May-Leonard type). First, we derive the global phase diagrams of attractors in the parameter space including the system size, where transition lines between simple attractors are clearly obtained in accordance with the results of linear stability analysis, but the transition borders become complex when multi-basin structures appear. The complex aspects of the transition borders are studied in the case when the system size decreases. Next, we show the statistical aspects of the turbulence with special attention to the onset of the supercritical Hopf bifurcation. Several characteristic quantities, such as correlation length, correlation time, Lyapunov spectra and Lyapunov dimension, are investigated in detail near the onset of turbulence. Our data show the critical scaling law near the onset only in the restricted parameter domain. However even when the critical indices are not determined accurately, it is shown that the empirical scaling relations are obtained in a wide parameter domain far from the onset point and those scaling indices satisfy several relations. These scaling relations are discussed in comparison with the result derived by the phase reduction method. Lastly, we make a conjecture about the stability of an ecosystem based on the bifurcation diagram: the ecosystem obeying the Lotka-Volterra equation in the case of May-Leonard type is stabilized more as the system size increases. 相似文献
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The global bifurcation structure for a model of coupled nonlinear oscillators has been analysed numerically. It is shown that destruction of the two-torus preceding chaos is usually observed in this system. The critical surface of the invariant two-torus and its collapse in the course of rotation are firstly observed in a realistic differential equation system. A scaling property for the fine structure of phase-locking regions has also been confirmed. 相似文献
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The grazing bifurcation, stick phenomena and periodic motions in a periodically forced, nonlinear friction oscillator are investigated. The nonlinear friction force is approximated by a piecewise linear, kinetic friction model with the static force. The total forces for the input and output flows to the separation boundary are introduced, and the force criteria for the onset and vanishing of stick motions are developed through such input and output flow forces. The periodic motions of such an oscillator are predicted analytically through the corresponding mapping structure. Illustrations of the periodic motions in such a piecewise friction model are given for a better understanding of the stick motion with the static friction. The force responses are presented, which agreed very well with the force criteria. If the fully nonlinear friction force is modeled by several portions of piecewise linear functions, the periodically forced, nonlinear friction oscillator can be predicted more accurately. However, for the fully nonlinear friction force model, only the numerical investigation can be carried out. 相似文献